Numerical solution of transient, free surface problems in porous media

Vaughan R Voller, S. Peng, Y. F. Chen

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


The focus of this paper is the development of numerical schemes for tracking the moving fluid surface during the filling of a porous medium (e.g., polymer injection into a porous mold cavity). Performing a mass balance calculation on an arbitrarily deforming control volume, leads to a general governing filling equation. From this equation, a general, fully time implicit, numerical scheme based on a finite volume space discretization is derived. Two numerical schemes are developed: (1) a fatty deforming grid scheme, which explicitly tracks the location of the filling front, and (2) a fixed grid scheme, that employs in auxiliary variable to locate the front. The validity of the two schemes is demonstrated by solving a variety of one- and two-dimensional problems: both approaches provide predictions with similar accuracy and agree well with available analytical solutions.

Original languageEnglish (US)
Pages (from-to)2889-2906
Number of pages18
JournalInternational Journal for Numerical Methods in Engineering
Issue number17
StatePublished - 1996


  • Finite volume
  • Free surface
  • Mold filling
  • Numerical method
  • Polymer molding
  • Porous media


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